You may just explicitly write $R$ as $R=\exp(i\alpha J_x/\hbar)\exp(i\beta J_z/\hbar)\exp(i\gamma J_x/\hbar)$, or some other convention with signs and axes, and because $J^2$ commutes both with $J_x$ and $J_z$, it also commutes with any and arbitrarily ordered function of them including $R$.
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Luboš MotlDec 11 '12 at 18:33